Question

johnny’s Lunches is considering purchasing a new, energy-efficient grill. The grill will cost $47,000 and will be depreciated straight-line over 3 years. It will be sold for scrap metal after 5 years for $11,750. The grill will have no effect on revenues but will save Johnny’s $23,500 in energy expenses. The tax rate is 30%.

Required:

a. What are the operating cash flows in each year?

b. What are the total cash flows in each year?

c. Assuming the discount rate is 11%, calculate the net present value (NPV) of the cash flow stream. Should the grill be purchased?

Answer 1

If we assume a 5 year project we have the following CF schedule:

Particulars	Remark	0	1	2	3	4	5
Cost Savings	Given		$ 23,500.00	$ 23,500.00	$ 23,500.00	$ 23,500.00	$ 23,500.00
Depreciation	47000/3		$ 15,666.67	$ 15,666.67	$ 15,666.67
EBT	Cost savings-Depreciation		$   7,833.33	$   7,833.33	$   7,833.33	$ 23,500.00	$ 23,500.00
Tax	30% x EBT		$   2,350.00	$   2,350.00	$   2,350.00	$   7,050.00	$   7,050.00
EAT	EBT-Tax		$   5,483.33	$   5,483.33	$   5,483.33	$ 16,450.00	$ 16,450.00
Depreciation	Added back as non cash		$ 15,666.67	$ 15,666.67	$ 15,666.67
OCF	EAT+Depreciation		$ 21,150.00	$ 21,150.00	$ 21,150.00	$ 16,450.00	$ 16,450.00
FCINV	Given	$ -47,000.00
Salvage							$ 11,750.00
Tax on profit on salvage value							$ -3,525.00
FCF	OCF+FCINV+Salvage+Tax on profit on salvage	$ -47,000.00	$ 21,150.00	$ 21,150.00	$ 21,150.00	$ 16,450.00	$ 24,675.00

As the entire machine was depreciated to 0 in year 3, the entire salvage value is profit which is an inflow while the tax paid on it is an outflow

NPV is calculated below:

Year	CF	Discount Factor		Discounted CF
0	$         -47,000.00	1/(1+0.11)^0=	1	1*-47000=	$         -47,000.00
1	$          21,150.00	1/(1+0.11)^1=	0.900900901	0.900900900900901*21150=	$           19,054.05
2	$          21,150.00	1/(1+0.11)^2=	0.811622433	0.811622433244055*21150=	$           17,165.81
3	$          21,150.00	1/(1+0.11)^3=	0.731191381	0.73119138130095*21150=	$           15,464.70
4	$          16,450.00	1/(1+0.11)^4=	0.658730974	0.658730974145*16450=	$           10,836.12
5	$          24,675.00	1/(1+0.11)^5=	0.593451328	0.593451328058559*24675=	$           14,643.41
				NPV = Sum of all Discounted CF	$           30,164.10

At times the machine is depreciated according to the accounting method whereas actual production continues.